Question

Tony sold 150 donuts in the first six hours in the day it was open. Every hour they sold six more donoughts the previous hour how much donuts were sold the first three hours

Answer 1

We are told donut sales is described by an arithmetic sequence of 6 terms whose sum is 150 and common difference is 6. If we split this sequence into two groups of 3 terms, the sum of the first group will differ from the sum of the second group by
  (number of terms)²×(common difference) = 3²×6 = 54

Then if x represents the number of donuts sold in the first 3 hours, the total number of donuts sold is
  x + (x + 54) = 150
  2x = 150 - 54
  x = 96/2 = 48

The number of donuts sold in the first three hours is 48.